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Pascal’s Triangle By Jessica Yaemmongkol

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Pascal’s Triangle

By Jessica Yaemmongkol

HistoryPascal was not the first to study the patterns on the

triangle. The reason the triangle was named after him was because he was able to discover the

importance of the entire pattern, with the help of a French mathematician , Pierre de Fermat.

Al-Karaji of

Persia

Yanh Hui of

Ancient

China

Yanh Hui’s Triangle

Page 3: Pascal’s Triangle By Jessica Yaemmongkol. History Pascal was not the first to study the patterns on the triangle. The reason the triangle was named after

Building the Triangle

To create the triangle start with the number 1.

To get the bottom number, add the top two numbers.

Page 4: Pascal’s Triangle By Jessica Yaemmongkol. History Pascal was not the first to study the patterns on the triangle. The reason the triangle was named after

Sequences and Patterns

Diagonals

Page 5: Pascal’s Triangle By Jessica Yaemmongkol. History Pascal was not the first to study the patterns on the triangle. The reason the triangle was named after

Sequences and Patterns

Odd and Even

If you color all the odd

numbers in the triangle you

will get a pattern that

similar to Sierpinski

Page 6: Pascal’s Triangle By Jessica Yaemmongkol. History Pascal was not the first to study the patterns on the triangle. The reason the triangle was named after

Sequences and Patterns

As you go down the triangle the sum of

the horizontal numbers doubles

Power of 2

Page 7: Pascal’s Triangle By Jessica Yaemmongkol. History Pascal was not the first to study the patterns on the triangle. The reason the triangle was named after

Sequences and Patterns

Start at a 1 on the left side, go up and to the right.

Add up the numbers and you get the Fibonacci sequence

Page 8: Pascal’s Triangle By Jessica Yaemmongkol. History Pascal was not the first to study the patterns on the triangle. The reason the triangle was named after

Purpose of Pascal’s TriangleTo determine the probability of a

coin landing on heads or tails.◦For example, if you toss a coin twice

you can have four different combinations

Probabilit

y HH

HT THTT

Or 1,2,2,1on Pascal’s triangle

Formula for combination

Page 9: Pascal’s Triangle By Jessica Yaemmongkol. History Pascal was not the first to study the patterns on the triangle. The reason the triangle was named after

Purpose of Pascal’s Triangle

(x+4)4 = 1x4 + 4x3 + 6x2 + 4x + 1

Binomial Expansion

Page 10: Pascal’s Triangle By Jessica Yaemmongkol. History Pascal was not the first to study the patterns on the triangle. The reason the triangle was named after

Credits

Pictures credited by

“Pascal’s Triangle.” Math is Fun. 2011 Mathisfun.com. 13 March 2011. <http://www.mathsisfun.com/pascals-triangle.html>.

http://www.mathsisfun.com/pascals-triangle.html

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